Taylor was dismissed for 129 close to stumps as the Black Caps reached 6-307 after being asked to bat on a green Basin Reserve pitch.
With the surface quickly losing its early fizz, a ragged West Indies effort in the field allowed Taylor to dominate the opening day, as he did in last week's drawn Test in Dunedin.
Kirk Edwards' grassing of a Taylor edge at third slip when he had yet to score proved critical as the former skipper unfurled a 227-ball stay featuring 15 fours.
Pace bowlers Tino Best and Darren Sammy also spilled chances after Taylor had reached three figures but they were let off when Shane Shillingford took a tremendous tumbling outfield catch to dismiss him for the first time this series.
The 29-year-old scored unbeaten knocks of 217 and 16 last week and his 362 runs before losing his wicket is a series record for a New Zealander, surpassing former captain Stephen Fleming's 343 in Sri Lanka 10 years ago.
Taylor also moved ahead of Fleming when raising his 10th Test century - the fourth-most by a New Zealander.
It has lifted his average to 46.52 from 52 Tests, the best by any Black Cap who has played more than 10 Tests.
He became the seventh player to surpass 4000 runs and the second-quickest to do so after Martin Crowe.
Upon reaching three figures, Taylor reserved a wave to parents Neil and Ann, who annually travel from Masterton to watch Wellington Tests.
"I haven't scored one here for a while (2009), so nice to give them a hundred. It's nice when the boss gives them time off and it's for a good reason," he said.
Taylor's knock was vital following the early loss of openers Peter Fulton (six) and Hamish Rutherford (11) - both caught by wicketkeeper Denesh Ramdin.
Taylor built substantial partnerships with Kane Williamson (45), Brendon McCullum (37) and Corey Anderson (38) against an attack largely lacking penetration.
Williamson, who missed the Dunedin Test with a fractured thumb, looked comfortable before sparring an edge to captain Sammy at second slip off Best.
McCullum chipped a lazy catch to short midwicket off Narsingh Deonarine while fellow-offspinner Shillingford claimed Anderson's scalp off from a faint edge when sweeping.
The spinners dominated the late stages as the tourists sought to remedy a slow over rate.
As was the case in Dunedin, the West Indies seam bowlers were too loose to fully exploit helpful early conditions.
Best was erratic but recorded the best figures of 2-66 off 14 overs while seamer Shannon Gabriel claimed Taylor's wicket - his first of the series.
Wicketkeeper BJ Watling was on eight and Tim Southee nine at stumps.